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We derive and interpret some relations between the luminosity, mass, and agedistributions of star clusters, denoted here by phi(L), psi(M), and chi(tau),respectively. Of these, phi(L) is the easiest to determine observationally,whereas psi(M) and chi(tau) are more informative about formation and disruptionprocesses. For populations of young clusters, with a relatively wide range ofages, phi(L) depends on both psi(M) and chi(tau) and thus cannot serve as aproxy for psi(M) in general. We demonstrate this explicitly by fourillustrative examples with specific forms for either psi(M) or chi(tau). In thespecial case in which psi(M) is a power law and is independent of chi(tau),however, phi(L) is also a power law with the same exponent as psi(M). Weconclude that this accounts for the observed similarity between phi(L) andpsi(M) for the young clusters in the Antennae galaxies. This result reinforcesour picture in which clusters form with psi(M) propto M^{-2} and are thendisrupted rapidly at a rate roughly independent of their masses. The mostlikely disruptive process in this first stage is the removal of interstellarmatter by the energy and momentum input from young stars (by photoionization,winds, jets, and supernovae). The few clusters that avoid this "infantmortality" are eventually disrupted in a second stage by the evaporation ofstars driven by two-body relaxation, a process with a strong dependence onmass. We suspect this picture may apply to many, if not all, populations ofstar clusters, but this needs to be verified observationally by determinationsof psi(M) and chi(tau) in more galaxies.Comment: Ten pages. Astrophysical Journal. Submitted 2005 October 20. Accepted  2006 August 15. V2--Minor improvements for consistency with published articl

Relations between the Luminosity, Mass, and Age Distributions of Young Star Clusters